Free Trig Function Calculator

This online trigonometric functions calculator automatically returns the values of all six standard trig functions—sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot)—when an angle is entered in either degrees or radians. It works as a sin cos tan calculator as well as a full six trig functions calculator, offering a convenient trigonometry calculator online for quickly finding trig values.

Defining the Six Functions with a Right Triangle

The most intuitive starting point for these functions is a right triangle. Considering an acute reference angle $\alpha$ inside such a triangle, the three sides are named in relation to that angle:

• Hypotenuse: The side opposite the right angle, which is always the longest side.
• Opposite: The side directly opposite $\alpha$.
• Adjacent: The side that lies between $\alpha$ and the right angle.

The three primary trigonometric functions are then expressed as ratios of these sides:

$$\sin(\alpha) = \frac{\text{Opposite}}{\text{Hypotenuse}}, \qquad \cos(\alpha) = \frac{\text{Adjacent}}{\text{Hypotenuse}}, \qquad \tan(\alpha) = \frac{\text{Opposite}}{\text{Adjacent}}.$$

These ratios form the foundation of trigonometry, enabling you to relate angles to side lengths.

Reciprocal Functions

The remaining three trigonometric functions are defined as the reciprocals of the primary ones:

$$\csc(\alpha) = \frac{1}{\sin(\alpha)} = \frac{\text{Hypotenuse}}{\text{Opposite}}, \qquad \sec(\alpha) = \frac{1}{\cos(\alpha)} = \frac{\text{Hypotenuse}}{\text{Adjacent}}, \qquad \cot(\alpha) = \frac{1}{\tan(\alpha)} = \frac{\text{Adjacent}}{\text{Opposite}}.$$

These reciprocal functions complete the set of the six fundamental trigonometric functions.

Reference Values for Common Angles

For some frequently encountered angles, the trigonometric values follow simple patterns. The table below lists the exact and approximate values for $45^{\circ}$.

Angle	$\sin$	$\cos$	$\tan$	$\csc$	$\sec$	$\cot$
$45^{\circ}$	$\frac{\sqrt{2}}{2} \approx 0.7071$	$\frac{\sqrt{2}}{2} \approx 0.7071$	$1$	$\sqrt{2} \approx 1.4142$	$\sqrt{2} \approx 1.4142$	$1$

At $45^{\circ}$, sine equals cosine, and as a result secant equals cosecant; tangent and cotangent both equal $1$.

How to Use the Trig Function Calculator

To obtain the trigonometric values for any angle, simply enter the angle magnitude and select the appropriate unit (degrees or radians). The tool instantly computes all six functions, providing both exact expressions where applicable and decimal approximations. This makes it a handy online resource for students, engineers, and anyone needing quick trigonometric evaluations.